Comeback kids: an evolutionary approach of the long-run innovation process

We provide a theoretical framework to understand when firms may benefit from exploiting previously abandoned technologies and brands. We model for the long run process of innovation, allowing for sustainable diversity and comebacks of old brands and technologies. We present two extensions to the logistic and Lotka-Volterra equations, which describe the diffusion of an innovation. First, we extend the short-term competition to a long-term process characterized by a sequence of innovations and substitutions. Second, by allowing the substitutions to be incomplete, we extend the one-dimensional process to a tree-form multidimensional one featuring diversification throughout the long-term development.